Two New Domain Decomposition Solvers
Einar M. Ronquist (Nektonics, Inc.)
We present two new domain decomposition solvers in
the context of spectral element discretizations.
The first is a domain decomposition solver for the
discrete steady convection-diffusion equation, while
the second is a domain decomposition solver for the
discrete steady Stokes or Navier-Stokes equations.
The solution algorithms are both based on the
additive Schwarz method in the context of
nonoverlapping subdomains. The key ingredients are:
(i) a coarse global system; (ii) a set of local,
independent subproblems associated with the subdomains
(or spectral elements); (iii) a system associated with
the unknowns on the subdomain interfaces;
and (iv) a Krylov method such as the CG algorithm
or the GMRES algorithm. We present numerical results
that demonstrate the convergence properties
of the new solvers, as well as the applicability
of the methods to solve heat transfer and incompressible
fluid flow problems.